US 3906509 A Abstract An antenna including a support having a conductive outer surface serving to support one or more bays of multifilar helical or spiral conductors with the conductors of each bay fed from the same end and serving to radiate substantially circularly polarized radiation broadside to the antenna.
Claims available in Description (OCR text may contain errors) United States Patent [1 1 DuHamel 51 Sept. 16, 1975 CIRCULARLY POLARIZED HELIX AND SPIRAL ANTENNAS [76] Inventor: Raymond H. Dul-Iamel, 1200! Rhus Ridge Rd., Los Altos Hills, Calif. 94022 [22] Filed: Mar. 11, 1974 [2]] Appl. No.: 449,946 [52] US. Cl. 343/895 [5 [J Int. Cl. H01Q 1/36 [58] Field of Search 343/895 [56] References Cited UNITED STATES PATENTS 3,0l9,438 1/1962 Pan .4 343/895 1629,93? l2/l97l Fredriksson et a1. 343/895 Primary Examiner-Eli Lieberman Azlomey, Agent, or FirmFlehr, Hohbach, Test. Albritton & Herbert ABSTRACT An antenna including a support having a conductive outer surface serving to support one or more bays of multifilar helical or spiral conductors with the conductors of each bay fed from the same end and serving to radiate substantially circularly polarized radiation broadside to the antenna. 15 Claims, 19 Drawing Figures PATENTEU SEPISIQYS '3, 906,509 sum 1 n; 3 4 TURN BIFILAR HELIX FEED POINTS W INSULATOR ll I J PATENTEBSEP I6 5975 saw 2 or a FIG. 4A F/G. 4B PATENIEU SEP 1 5 ms SHEET a 0 3 PATENTEU SEP I s 1915 SHEET 5 I]? M COS IN RADIANS'CIRCUMFERENCE IN WAVELENGTHS 7 IN RADIANS'CIRCUMFERENCE IN WAVELENGTHS PATENTEDSEP Isms 3.906.509 swamps I 3 4 T P F/G. l/A Fla H5 PATENTEU 1 5 3 #3 GE; 5560 am 7 as a; 6=90 z HOLDS FOR CYLINDER 9 DIAMETER OF 0: MODE 3, 4 WIRE .08 TO 24A 2 Ed E D I.oo O l l l l l l 0 I0 20 30 4o 50 so 70 PITCH ANGLE, w F/G /ZA 9=90 2.0- CYLINDER DIAMETERS o OF .057 T016! A m MODE 2, 2 WIRE LU 2 1 L0- I O l l l I l l 0 IO 6O 7O PITCH ANGLE, a F/G. /Z5 lOdb 'ZOdb CIRCULARLY POLARIZED HELIX ANI) SPIRAL ANTENNAS BACKGROUND OF THE INVENTION This invention relates generally to helix and spiral antennas, and particularly to circularly polarized helix and spiral antennas and more particularly to such antennas for FM and TV broadcast. As used herein. circularly polarized helix antenna is used to refer to the general class of elliptically polarized antennas with a low axial ratio. Helical antennas for VHF and UHF television channels are known. Such antennas have comprised one or more bays each including a pair of single conductors helically wound about a conducting mast which supports the antenna. The conductors are contrawound, extend in opposite directions and are excited at the common point. The radiated signal is substantially horizontally polarized. Wheeler. Proceedings of The IRE. page I484. I947, describes a circularly polarized multifilar helix which has a doughnut shaped radiation pattern. The maximum dimensions of the helix are restricted to be less than the radian length, i.e.. less than M211, where A is the wavelength. The turns are of a resonant length (standing waves) and the elements of the multifilar helix are all fed in phase from a common point. No conditions are stated or any provisions made for incorporating a central conducting support mast. Kraus. Proceedings of the IRE, page 263. 1949, describes a single wire helix which can be operated in the circularly polarized normal mode or axial mode. In the axial mode. the turn length is considerably less than a wavelength so that it produced a doughnut shaped pattern. In the beam mode. the turn length is about one wavelength and the radiation pattern is endfire. Higher order modes where the turn length is approximately M wavelengths. where M is an integer, are mentioned. No mention is made of multifilar helices or supporting con ducting masts. Kilgus. IEEE Transactions on Antennas and Propagation. page 349. May 1969. shows how bifilar and quadrifilar. fractional turn. resonant helices can be fed in mode one to produce endfire circular polarization. The bifilar elements were fed in antiphase and the quadrifilar elements were fed in quadrature. The axial length and diameter of the helices was only 0.27 A and 0.09 A. A conducting cylindrical balun was used to support the helices. Its diameter was only about 0.03 A. Adams. IEEE Transactions on Antennas and Propagation, page 547, July l97l. describes a multi-turn quadrifilar helix operating in mode one with a dielectric or conducting cylinder within the helices. Emphasis is placed on the frequency scanning of the beam direction. Neureuther et al. IEEE Transactions on Antennas and Propagation, page 203. March I967. present solutions for the propagation constant of modes 1 and 2 for a sheath helix with a conducting core (cylinder). No mention is made of using multiple conductors to approximate the higher order modes. No discussion or theory is presented to determine the polarization characteristics of helices for various pitch angles and cylinder diameters for the various modes. Dyson and Mayes. IRE Transactions on Antennas and Propagation, V. AP-9, pp. 334-342. July I961. describe multiple conductor conical log-spiral antennas excited in various modes associated with the structure. It is noted that the radiated fields are predominantly circularly polarized. It is pointed out that the maximum radiation is approximately normal to the axis of the spiral for a four arm spiral fed in mode 2. However, these antennas have very low gain and a wide beamwidth in the elevation plane. This results because the pitch angle is constant along the cone and thus the turn length is proportional to the distance from the vertex. Conducting cones or cylinders inside the conical spiral have been avoided or minimized since they degrade the performance of the antenna. OBJECTS AND SUMMARY OF THE INVENTION It is an object of the present invention to provide a multifilar helix or spiral antenna suitable for radiating circularly polarized radiation. It is another object of the present invention to provide a high gain omni-directional antenna for radiating circularly polarized radiation over moderate frequency bands. It is another object of the present invention to provide circularly polarized broadcast television antennas which improve the quality of television reception. It is another object of the present invention to provide an antenna which includes a plurality of helices wrapped about a vertical supporting structure having a conductive surface with the helices placed and adjusted such that the radiation pattern is omni-directional and broadside and the radiation is circularly polarized. The foregoing and other objects of the invention are achieved by an antenna comprising a support having a conductive outer surface with at least two conductors spaced from said surface and helically wound about the surface with a pitch angle which is greater than 25 with means for supporting the helices from the support and means for feeding one end of each of said conductors with voltages of equal magnitudes and of predetermined phase. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 schematically shows a two bay antenna array with each bay including multifilar helices in accordance with the invention. FIG. 2 is an enlarged view of the lower end of one of the bays showing the antenna feed detail. FIG. 3 is a helix current sheath model of an antenna useful in explaining the operation of antennas in accordance with the invention. FIGS. 4A and 4B show a single turn helix and developed cylinder useful in explaining the operation. FIG. 5 shows a continuous current ring useful in explaining the operation. FIG. 6 shows the axial ratio for several pitch angles as a function of observation angle. FIG. 7 shows the axial ratio as a function of beam direction for two pitch angles. FIG. 8 shows the phase error and the degradation of the axial ratio as a function of the circumference of the support for various operating modes. FIG. 9 shows the axial ratio as a function of the circumference of the helix sheath for various support circumferences and operating modes. FIG. 10 shows a portion of a quadrifilar helical antenna. FIGS. IlA-C are schematic diagrams of feed networks for modes 3, 4 and 5. DESCRIPTION OF PREFERRED EMBODIMENTS An antenna in accordance with the invention is schematically shown in FIGS. 1 and 2. The antenna is a twobay helical antenna with each bay including bifilar windings. Referring more specifically to the figures, each bay of the antenna comprises a supporting mast 11 which may be a hollow pipe or tube, shown more clearly in FIG. 2, through which a coaxial feed line 12 may extend to feed the ends of the helices. More particularly, the bifilar helices are shown at 13 and 14 spaced physically 180 apart. In this particular instance, the helices are shown as a four-turn bifilar helix where the feed system point is shown in more detail at 16 in FIG. 2. The helices have a pitch angle ill which is selected in accordance with the invention to provide circularly polarized radiation as will be presently described. The currents I, and l, are shown fed to the end of the helix. A transmission-line type feed network is illustrated more clearly in FIG. 2. The transmission lines are formed by rods or strips placed above conductive disc 18 which supports the adjacent end of the antenna. The helix rod characteristic impedance is in the order of 200 ohms. The inner conductor of the coax is connected to the I ohm line 19 which includes quarter wavelength transformers 2] and 22 coupling the energy to the lower end of the helical conductors l3 and I4. The parallel combination of the transformers and feed combination provides a 50 ohm impedance to the coax feed thereby providing an impedance match for the maximum transfer of energy from the coaxial line to the helical conductors. Spaced along the support 11 are dielectric discs or rods (not shown) which engage and support the helix turns. To generalize, each bay may consist of N end-fed helices which are spaced around the cylinder and are excited with voltages of substantially equal magnitude and with phases which depend upon the mode number, the number and the spacing of the helices. In order to understand how this is done, it is expedient to consider the helix current sheath model of FIG. 3 wherein the current flows helically along a unidirectionally conducting cylinder 26 spaced from a coaxial conductor 27. The current direction shown by the arrows 28 is at an angle 11 with respect to a circumferential line around the cylinder. The conductor 26 does not conduct in the direction transverse to the currents. The .x, y, z directions and the associated angles are labelled in FIG. 3. Referring particularly to FIG. 3, the definition of a mode number as used herein is the number of 360 linear phase changes of the current in one circumference such as shown at the line 29, assuming the helical sheath current I shown. Thus, if in traversing the circumference, the phase of the current progresses by 720, the mode number, M, is 2. In general, it can be stated that the current on the cylinder at Z 0 for mode M is given by u d). O) jM l I where M is a positive or negative integer. A constant term can be added to Md), but thus just corresponds to a rotation of the sheath. It is also assumed that there are only traveling waves on the sheath such that the current varies as where s is the distance measured along the current path as shown in FIG. 3 and k is the propagation constant for the current. For this case M is chosen to be negative. For the modes of interest here, It is approximately equal to the free space propagation constant B 21r/ A. It is assumed that k B in the following analysis. Under these conditions it may be shown that the current on the cylindrical surface varies as It will be noted from (3) that the phase of the current along a directrix of the cylindrical sheath varies linearly with Z. Thus, because of rotational symmetry, the sheath will radiate a conical beam in the direction 60 where sintli M cos 4; to. )=e I Bp-t +M cos 1') 4 Baaw i B0 cos The elevation width of the beam is inversely proportional to the length of the sheath. For a constant eleva tion angle 6, the phase of the radiated field varies as Md). For broadside radiation (60 it is seen that the argument of (4) should be zero, i.e., eostla=- [5) T: cos ill Thus, for radiation at (or near) broadside, it is seen from (5) that the turn length is (or nearly is) M wavelengths. Next, let us determine the conditions for obtaining elliptical polarization from the current sheath with a low axial ratio, i.e., a close approximation to circular polarization. The axial ratio may be measured by rotating a linearly polarized dipole antenna in a plane transverse to the direction of propagation. The ratio of the maximum received voltage to the minimum received voltage is defined to be the axial ratio. For circular polarization, the axial ratio is one (or zero db). For PM or TV broadcast, it is desired that the axial ratio be 3 db or less. Circular polarization is obtained when the vertical and horizontal components of the electric field have equal magnitudes and are 90 out of phase. The polarization characteristics in any direction for the complete current sheath will be the same as that for the short cylindrical ring of FIG. 5. Thus. we assume a continuous distribution of vertical and horizontal currents on the ring given by (81 We may perform an exact analysis of this model by making use of published formulas for vertical and horizontal dipoles near a conducting cylinder. The E9 component of the radiation pattern of a vertical current element, located at p p d) 0. Z may be written as J,,(W) is a Bessel Function of the First Kind N,.(W) is a Bessel Function of the Second Kind Similarly, the E9 and E a components ofa horizontal current element, lo at the same location are given by E I sin Osin ill (j)[J W M( I) where we substituted (7) for l Progressing in this manner. we find that sin 0 sin ill M cos ill cos 6/ cos ill where we have summed (9) and 10) to obtain the total If the cylinder is removed. then (14) reduces to It is enlightening to study (13) for this latter case where the cylinder is removed. Consider first the case when the beam is directed broadside and determine the axial ratio as a function of the observation angle. In this case B M cos ill and W ,Gp sin 0=M cos ill sin 6 I l7| Then I sin ill sin fl cos 6 Jmm E *1 sin 6 cos ill J \1'( 1) ('8, In order to achieve circular polarization (18) must equal eitherj or j. For this case where the functions are real, it is only necessary to have the magnitude of (18) equal to one. The axial ratio is simply this magnitude. The axial ratio is shown in FIG. 6 for several pitch angles as a function of the observation angle 6. This graph is for M 2. but is fairly accurate for all negative mode numbers. The axial ratio. AR, is infinite when the numerator of( 18) is zero, i.e.. when the E polarization is zero. For small pitch angles, this occurs approximately when Notice that the axial ratio is quite low for values of 0 removed more than 30 from the direction for which the AR is infinite. Thus, for circularly polarized radiation in the broadside direction. it is desirable to restrict ill to be greater than 25 if ill is in the first quadrant (0 to For ill in the second quadrant, ill should be less than for a low axial ratio. This very interesting property has not been pointed out previously and holds for all M. For ill in the first quadrant and waves traveling in the positive direction, the polarization is right circular near the zenith (6 0). For ill in the second quadrant. the polarization is reversed and is left circular near the zenith. The sense of the polarization reverses as 6 progresses through the direction at which the axial ratio is infinite. Thus. for ill in the first quadrant. the polarization is left circular near the nadir (6 and predominantly left circular at broadside except for small pitch angles. Notice that the AR is high for elevation angles nearly equal to the pitch angle. Next. consider the case where the helix diameter is adjusted to radiate a beam from the complete sheath in the direction 6,,. From 4 we find that and then (13) becomes (sin Ila cos 6 I sin 9,, cos I}: J...( 2) ud 2) (2|) where we have set the observation angle equal to 6,, because we are most interested in the AR in the direction of the main beam. FIG. 7 shows the AR in this direction as a function of the beam direction for two different pitch angles. It is seen that the numerator of (21) is zero when 90 :11. Thus, the helix will radiate a low AR circularly polarized beam only in directions removed from that given by 19) by at least about 25. A- gain, this holds for all M. Return now to the case where the cylinder is present. A study of (14) reveals that the expression inside the brackets is always real. Thus, if the phase of is 0 or 180 then the phase of EG/Ed is 90 or 90 which is correct for circular polarization. If the phase is not 0 or l80 then there is nothing we can do about it. We will have elliptical polarization. It may be shown that the phase of this ratio is given by tan 1 I( M( W|) 31 I M WI) J!" W!)) 1 FIG. 8 shows the phase of this ratio and the minimum axial ratio as a function of the cylinder circumference in wavelength modes for broadside radiation. (Actually the phase is given by 180 minus those values shown in the graph. However, the deviation from l80 is the important quantity). It is seen that for mode 1 with fip, 0.5 (p z M12) that the phase error is 20 and the minimum axial ratio (assuming E9 and E have equal magnitudes) is 3.1 db. The phase error is negligible for small cylinder diameters for all the modes. Assuming that phase errors greater than 20 are not tolerable for broadcast applications, the following empirical formula for the minimum cylinder circumference Bp, (measured in wavelengths) was derived from the theoretical results B M cos 25 0.5 Equation 13) has been evaluated for four modes for several cylinder diameters for broadside radiation in the broadside direction as a function of the helix pitch angle. FIG. 9 shows the axial ratio as a function of helix circumference for several cylinder circumferences for modes 1 through 4. It is seen that as Bp approaches M or tla becomes small that the axial ratio becomes large. If axial ratios on the order of 3 db are desired, then the pitch angle should be greater than 25 and the sheath circumference Bp must be less than M cos 25. Of course, the cylinder circumference must necessarily be less than the sheath circumference. The restriction (22) states that the cylinder circumference must be at least one-half wavelength less than this maximum sheath circumference. This corresponds to a spacing between the cylinder and sheath of 0.0796 A. in order to obtain sufficient radiation from the helix sheath, it is usually necessary to use spacings larger than this. Thus, the restriction that the pitch angle is larger than 25 implies that the cylinder diameter restriction (22) is satisfied. However, larger pitch angles and smaller cylinder diameters will normally be used in order to achieve low axial ratios. In FIG. 9 it is seen that when the cylinder diameter is larger than the value given in Table I, then the axial ratio is large for all helix radii. It is apparent from these results that the expressions (14) and (15) for G with and without the conducting cylinder are approximately equal for all modes provided that the cylinder diameter is less than the values given above. This is a very surprising and fortunate result that the insertion of the cylinder does not degrade the AR of the helix. It would be expected that for a cylinder diameter not small in wavelengths, that the reflection, diffraction and scattering of the radiation from the helix sheath by the cylinder would change the polarization of the helix sheath drastically. The axial ratio of the radiation in other directions from the sheath with the cylinder will behave in a manner similar to that for the sheath without the cylinder. This follows because the bracketed term of 13) causes an increase of axial ratio for other angles for either case. If the currents flow in the negative Z direction (i.e., fed from the top), this changes the sign of the azimuthal phase variation but does not change the sense of polarization. Thus, in order to achieve an omnidirectional radiation pattern, we must have a close approximation to a single traveling wave on the sheath helix. Otherwise, the pattern will be of the form 1 h cos Mq where b depends upon the relative magnitudes of the two traveling waves. Having determined the conditions for achieving broadside, omnidirectional circularly polarized radiation, let us now determine a practical approximation to the sheath helix. An obvious approximation would be to use a large number of closely spaced helical conductors to approximate the unidirectionally conducting sheath helix. One approach would to be use N equally spaced identical helical conductors and excite them with voltages given by (assuming the helices all originate on the same transverse plane) Another more general approximation is to use N unequally spaced helices where their placements are defined by d) The voltage excitations are then given by In this case the input impedances are not equal (except for a few special cases) and it is considerably more difficult to achieve the desired currents. For a given number of N equally spaced helices, there are a multiplicity of mode numbers M which lead to the same excitation coefficients (23). These modes are given by where k is an integer. However, the helix diameters or turn lengths for these modes are quite different for the condition of broadside radiation. In the following dis cussion, which is oriented towards television broadcast antennas with broadside radiation, designation of a mode M helix implies that the turn length is approximately M wavelengths. Practically speaking, we would like to minimize the number of helices for a given mode without degrading the gain, beam width, polarization and omni pattern compared to that of the sheath helix. The gain, pattern and polarization could be degraded by not using enough helices. We can estimate the minimum number of helices by making use of conventional antenna array theory. For a long multifilar helical antenna with L turns of each helix, we may assume that it is equivalent to a linear array ofN x L single turn, equally spaced helices wrapped around a cylinder. The helix elements do not begin or end at the same place with this approximation. Each single turn helix does not have a directive pattern because of the way the wire wraps around the cylinder. Thus, we must invoke the usual array condition for preventing grating lobes. For isotropic radiators, it is usually specified that the element spacing is somewhat less than a wavelength. For helices with mode numbers greater than one (which we are interested in for broadcast applications), there is no radiation along the axis of the sheath. Thus, we may safely specify that the element spacing is not greater than the wavelength. Since the element spacing is given by MA sin ill/N, we have as our restriction that The values of 11 that are usually used are less than 50 to 60. Experimental results have shown that the patterns, gain and polarization are not degraded for N M for modes 2 through 4. Reflections from the ends of the helices degrade the omnidirectional pattern and can cause severe distortions of the picture in TV broadcast applications for the following reason. The phase of the reflected traveling waves at the ends of the helices change with respect to the incident traveling waves at the feed points over the frequency range of the visual signal because of the fixed time delay through the helix wires. This causes amplitude and phase distortions of the transmitted signal for a fixed azimuth angle, i.e., the aximuthal pattern changes over the visual frequency band. it is desirable to keep the reflected waves more than 20 db down for the VHF channels. This is quite difficult to do if the helix bay length is only a few wavelengths long since it is not possible to obtain enough attenuation by radiation. Several techniques may be used to approximate or simulate a traveling wave condition for the helix current. The attenuation of the current on the helix is inversely proportional to the pitch angle, I11. The beamwidth and bandwidth requirements may make it possi ble to choose ll! such that the one way attenuation through the helix is greater than about 20 db. In this case, the reflected waves at the end of the helices will be small so that the pattern is nearly omnidirectional. For those cases where the one-way attenuation is less than about 20 db, we may place matching devices, such as series or shunt capacitors or inductors, near the ends of the helix wires. These will reduce the magnitude of the reflected waves and, therefore, improve the omni pattern. However, there will be some radiation from the standing waves on the ends of the helices which will spoil the omni pattern. The ends of the helices may be left hanging or shorted to the cylinder for lightning protection. We may make use ofa unique property of multifilar helices to simulate a traveling wave condition. The reflected power may be radiated into the upper hemisphere by using a helix with 2M/N not equal to an integer. [f the helices are ofequal length, the reflected cur rents, as viewed from the other end, will have a phase progression of 21rM/N rather than Z'n-M/N. We may designate this as mode -M. It will be different than mode M if M# MIkN or rearranging 2M/N ii i k Thus, the condition that 2M/N is not an integer ensures that the reflected wave is a different mode. This condition eliminates N 2, N M and N M/2. For broadside radiation, the phase progression from helix to helix along a direetrix in the positive Z direction is given by 41rlM |/N radians for the reflected wave. The reflected wave radiates a beam in the direction 6, given by sin ab where I: is an integer. The pitch angle and/or N can be chosen for a given mode number such that there is only one value of 0,. in the visible range. Then the helix may be fed from the end (top or bottom) that lets the reflected power radiate in the upper hemisphere. If the one-way attenuation through the helix is greater than 10 db, then only a few percent of the power is wasted. Another way of eliminating the reflected wave is to use terminating resistors at the ends of the helices. However, the above radiation approach is more economical and reliable. Another very important reason for restricting 2M/N from being an integer is that it is possible to obtain a much lower VSWR over a given frequency bandwidth than for the case where this ratio is an integer. The progressive helix phasings given in (23) are usually achieved by means of corporate or parallel feed net works wherein the desired phasings are obtained by delay lines in the various branches of the feed network. Waves reflected from symmetrical points on a multifi lar helix, such as the feed points or ends of the helices, will arrive back at the single feed point of the feed network with phasings given by twice the phases of the voltages given by (23). It is easily shown that the sum of the reflected waves at this feed point is zero unless ZM/N is an integer. If it is an integer, the reflected waves add in phase and the VSWR is much higher. This technique of cancelling reflections has been used in 4 sided broadcast antennas where adjacent elements are fed in quadrature. but not in this more general case of multifilar helices. FIG. illustrates a portion of an end-fed quadrifilar helical antenna with equal spacing of the helices and a constant pitch angle. It is obtained by adding two helices to the bifllar helix of FIGS. 1 and 2. Table 1 lists the phases of the helix currents for modes 3 through 6. For each mode, the pitch angle should be restricted according to (26) so that grating lobes are not formed. Modes I and 2 are not included since four conductors are not needed for these modes. Modes 7 etc. are not included since the pitch angle is restricted by (26) such that the axial ratio is high. Modes 3 and 5 are preferred since they have the desired omnidirectional and low VSWR characteristics described above. TABLE I Phases of Helix Currents for Ouadrifilar Helix Schematic diagrams of feed networks for modes 3, 4 and 5 are shown in FIG. 11. The single lines represent transmission lines, i.e., coax, microstrip, etc. For mode 3, a parallel feed is shown wherein the desired phasings are obtained by additional line lengths or delay lines. For the corporate feed network for mode 4, two of the Tjunctions are displaced 90 along the lines so that reflections from these Ts cancel at the input port. For mode 5, a corporate feed is shown wherein the Ts are offset from the centerlines in order to obtain the desired phasings. In addition, two Ts are displaced 90 so as to cancel reflections. For this feed reflections from the helix discontinuities cancel at the first T junction. For FM and TV broadcast it is desirable to have the VSWR of antennas less thanl.l:l over the channel bandwidth in order to control picture and sound distortions (due to multiple reflections) to a reasonable level. In order to achieve this, it will usually be necessary to place M4 transformers and/or transmission lineswiih different characteristic impedances in the feed network so as to have a matched system throughout. In some cases it may be desirable to place a N4 transformer in the helix structure next to the feed network. The feed network may be placed in or around the cylinder or on a disc attached to the cylinder. The characteristic impedance of each helical element may be estimated as follows. Assume the x11 angle is large so that the capacitance between the helix and cylinder is about equal to that between two parallel cylinders of unequal diameters. Neglecting the presence of the other helices we would then compute the characteristic impedance of one helix to the cylinder as where p, cylinder radius p helix radius r helix wire radius This impedance will be on the high side for reasonable pitch angles. On the low side we may assume that the characteristic impedance is the same as that of the helix wire spaced a distance (p p from an infinite ground plane. The actual characteristic impedance may fall outside these limits because of mutual coupling effects between adjacent helices. The input impedance of each helix will be close to its characteristic impedance if we establish a close approximation to a single traveling wave on the helix near the feed point. The extension of these concepts to other configurations for different mode numbers is straightforward now. A particularly useful configuration for the low VHF channels (and multi-channel FM antennas) is a 3 wire mode 2 antenna wherein the progressive phasing between helices is 240. Modes 3 and 4 with N 4 and 3 respectively would be most useful for the upper VHF channels. For the UHF channels, modes 4 and higher would be used with N set somewhat less than the mode number according to (25). The axial ratio of a helical antenna will be larger than that predicted from the above theory. The reason for this is that there will be some radiation from the feed point region and any shorts to ground at the end of the helices. Thus, the helical antenna should be designed for an axial ratio about one or two db less than required. This radiation may also degrade the omnipattern. One limit on the length of a multifllar helical antenna bay is due to the beam scanning with frequency. If the beam scans an appreciable fraction of the bay beamwidth over the channel bandwidth (or frequency band). then there will be an appreciable change in gain for a given elevation angle. Again this could cause dis tortion of transmitted picture for TV. For a bottom fed helical bay, the direction of the main beam is given by sin ll! where f,, is the frequency for which the beam is broadside (0,, 90). This holds for all modes. 6,, decreases with increasing frequency. Broadcast regulations require that at least half the radiated power is radiated below the horizon. Thus,f,, should be set equal to the highest frequency in the channel. It is found from (29) that for ill 35, that the beam direction scans I per 1 percent change in frequency. Thus, for channel 2, the beam for a single end fed helix would scan below the horizon at the low end of the channel. This would limit the helix to less than two wavelengths. For this short of a helix it would be quite difficult to achieve traveling waves on the helices and, therefore, omni patterns and a low VSWR. This difficulty can be circumvented by using several bays of helices with a special feed network. The lengths of the lines in the feed network are adjusted so that the array pattern for the bays scans with frequency in a direction opposite to that for the individual patterns. Since the total pattern is equal to the product of the array pattern times the bay pattern, it is possible to choose the feed network so that the total pattern scans a negligible amount over a television channel. The beam broadens and the gain decreases slightly at the band edges. Computations were performed for two bays of helices using mode 2 with three wires where the individual bay length was 3A at midband. The power was equally divided between the two bays by a Tjunction. The length of the transmission line to the upper bay was one wavelength shorter (at midband) than the line to the lower bay. For an average pitch angle of 37, it was found that the beam scan was negligible over an 8 percent bandwidth and the gain reduction was only 0.5 db at the band edges. Experimental and theoretical results show that the helix current decays exponentially away from the feed point for a uniform helix (where the diameter and pitch angle are independent of Z). If the one-way attenuation is more than ID or I2 db, then the elevation patterns of a bay are unsatisfactory in the sense that the gain is reduced and the side lobe levels are increased over that of a uniformly illuminated aperture. Measurements have shown that the attenuation of the helix current per unit length is approximately inversely proportional to the pitch angle. FIG. 12 shows the variation of the attenuation versus the pitch angle for modes 2 and 3 with 2 and 4 wires respectively. These curves are for the case where helix diameter is constrained so that the turn length is independent of I11 and also so that the radiation is broadside. It was surprisingly found that the attenuation was insensitive to cylinder diameter over a range of diameters. Leaky wave antenna principles (Jasik, Antenna Engineering Handbook". McGraw-Hill, 1961, Chapt. l6) may be used to design a constrained variable pitch angle helix antenna to produce a wide range of antenna patterns. The design procedure makes use of the fact that the power radiated per unit length is proportional to the product of the attenuation constant and the incident power at that point. For broadcast coverage, we desire approximations to cosecant patterns or conventional beam patterns with null fill and a beam tilt. A simple approximation to a uniform aperture is to constrain the helix so that it lies on a conical surface such as shown in FIG. 13. The helix is fed from the bottom so that the pitch angle decreases with distance from the feed point. The turn length is constrained to be approximately M wavelengths so that the radiation is approximately broadside. The relation between distance, s. along the spiral and angle dz is then (15 We may integrate (32) to obtain the relation between r and s, 3 (21m sin 2) sin( sin m x r.- 4; sin B 21rsin E (33) The tapered helix is somewhat similar to the conical spiral of Dyson and Mayes. However, Dyson's spiral has a fixed pitch angle and tapered turn length, whereas this helix has a tapered pitch angle and a fixed turn length. A Mode 3, 4 wire helix antenna was constructed in accordance with the foregoing for operation at 738 MHz (wavelength of l6 inches) with a support mast diameter of 2.5 inches. The helices were 5 turn tapered helices where the pitch angle varied from to 30 and the helix diameter from 5.72 inches to I32 inches. The helix length was l2 feet. The helices were fed 0, 270, I' and The resulting radiation patterns are shown in FIGS. 14 and 15 where FIG. 14 shows the vertical pattern and FIG. 15 the horizontal pattern. The design of a multifilar helix antenna to produce circularly polarized omnidirectional radiation for television or FM broadcast applications makes use of the preceding information and usually consists of the following steps: I. Determination of the Mode Number The diameter of the required support structures determines the minimum mode number that may be used. The diameter of the support structure may be deter mined from the height of the antenna (which is proportional to gain) and environmental conditions (mostly wind and ice loading and whether or not guys are used). In some cases the diameter may be determined or fixed by other considerations such as a fixed structure which the helix must be placed around. The mode number is chosen so that the helix circumference is about one-half wavelength greater than the support circumference for the largest pitch angle. ill to be used, In the interests of economy, the minimum value of M given by (34) should be used. Since I1! is usually about 60, the support circumference is considerably less than the maximum given by (22). Hence, the axial ratio degradation due to the support will be small. 2. Determination of Number of Bays It is desirable to minimize the number of bays of the antenna in order to minimize the cost of the feed network. The length of a single end fed bay is limited by the scanning of the bay beam with frequency. The amount of scan depends upon the pitch angle and espe cially on the bandwidth. The average pitch angle should be chosen to give about 15 db one-way attenuation through the helix. The total beam scan over the frequency band may be determined from (29). The maximum bay length can then be determined from the specified antenna gain variation over the frequency band. The number of bays is then set equal to the minimum number for which this length is not exceeded. 3. Determination of Pitch Angles The pitch angle is usually tapered over the length of a bay so as to approximate a uniform aperture distribution. The pitch angle is restricted to be greater than except possibly over a small percentage of the bay height in order to achieve a low axial ratio. The maximum pitch angle will usually be in the range of 60. 4. Determination of the Number of Helices The number of helices. N, is chosen to satisfy (26) and (27) as well as to minimize N. N would usually be set equal to 3 and 4 for modes 2 and 3 respectively. For the higher order modes N would be less than M1. The use of the novel circularly polarized helix anten nas of the present invention provide improvement in the quality of television reception for at least two reasons. First, the ghosts" due to delayed reflections from buildings and hills are reduced by using circularly polarized receiving antennas. Reflections from buildings and smooth hills have the property that the reflected wave has essentially the opposite sense of circular polarization as the incident circular polarization. The receiving antenna will reject this reflection by an amount which depends upon the axial ratio of both the transmitting and receiving antennas. Assuming an ideal receiving antenna with an axial ratio of l, the rejection of a reflection from a smooth surface is given by AR I Rejection 20 log ET where AR is the axial ratio of the transmitting antenna. Rejections for axial ratios of l, 3, 6 and 10 db are 24.8, 15.3, 9.6 and 5.7 db respectively. Thus, it is seen that it is quite important to keep the axial ratio of the transmitting antenna less than 3 db. Axial ratios less than 2 db have been achieved for a mode 3, 4 wire helix for all azimuth directions. The second reason is that many of the low cost television antennas, such as rabbit ears, respond to vertically polarized waves as well as, if not better than, horizontally polarized waves. The use of circularly polarized transmitting antennas would allow these receiving antennas to receive stronger signals regardless of their orientation. I claim: 1. An elliptically polarized helical antenna with low axial ratio comprising a support having a conductive outer surface, at least two conductors spaced from said surface and helically wound about said surface in the same direction, said conductors wound with a pitch angle greater than 25, means for supporting the helical conductors spaced from said surface, and means for feeding the adjacent end of each of said two or more conductors with voltages of substantially equal magnitude and having predetermined phase relationship whereby to excite said antenna in a selected mode, said helically wound conductors being unequally spaced around the support and the feed voltages are given by where n l, 2, ...N N the total number of helically wound conductors M the mode number, an integer, for mode M the phase of the radiated electric field varies with the azimuth angle, (b, as Md) for a constant elevation angle 0, and the magnitude of the electric field is essentially independent of the azimuth angle 11:. (1),, the angular placement of the n"' helically wound conductor about the support, all starting and fed at the same transverse plane. 2. An elliptical polarized helical antenna with low axial ratio comprising a support having a conductive outer surface, at least two conductors spaced from said surface and helically wound about said surface in the same directioon, said conductors wound with a pitch angle greater than 25, means for supporting the helical conductors spaced from said surface, and means for feeding the adjacent end of each of said two or more conductors with voltages of substantially equal magnitude and having predetermined phase relationship whereby to excite said antenna in a selected mode, said helically wound conductors being unequally spaced around the support and the feed voltages being selected whereby the voltages appearing on the conductors at the same transverse plane are given by where n l, 2, ...N N the total number of helically wound conductors M the mode number, an integer, for mode M the phase of the radiated electric field varies with the azimuth angle, b, as Md) for a constant elevation angle 6, and the magnitude of the electric field is essentially independent of the azimuth angle 1 the angular placement of the n" conductor in said transverse plane. 3. An elliptically polarized helical antenna with low axial ratio comprising a support having a conductive outer surface, at least two conductors spaced from said surface and helically wound about said surface in the same direction, said conductors wound with a pitch angle greater than 25, means for supporting the helical conductors spaced from said surface, and means for feeding the adjacent end of each of said two or more conductors with voltages of substantially equal magnitude and having predetermined phase relationship whereby to excite said antenna in a selected mode, said helically wound conductors being uniformly spaced around the support and starting at the same transverse plane and the feed voltages being given by where n l, 2, ...N M the mode number, an integer, for mode M the phase of the radiated electric field varies with the azimuth angle, (b, as M4) for a constant elevation angle 0, and the magnitude of the electric field is essentially independent of the azimuth angle dz, N total number of helical conductors 4. An elliptically polarized helical antenna with low axial ratio comprising a support having a conductive outer surface, at least two conductors spaced from said surface and helically wound about said surface in the same direction, said conductors wound with a pitch angle greater than 25, means for supporting the helical conductors spaced from said surface, and means for feeding the adjacent end of each of said two or more conductors with voltages of substantially equal magnitude and having predetermined phase relationship whereby to excite said antenna in a selected mode. said helically wound conductors being equally spaced around the support and the feed voltages being selected whereby the voltages appearing at the same transverse plane are given by where n l, 2, ...N M the mode number. an integer. for mode M the phase of the radiated electric field varies with the azimuth angle, 5, as M05 for a constant elevation angle 0, and the magnitude of the electric field is essentially independent of the azimuth angle 42, N total number of helical conductors 5. An elliptically polarized helical antenna with low axial ratio comprising a support having a conductive outer surface, at least two conductors spaced from said surface and helically wound about said surface in the same direction, said conductors wound with a pitch angle greater than 25, means for supporting the helical conductors spaced from said surface, and means for feeding the adjacent end of each of said two or more conductors with voltages of substantially equal magnitude and having predetermined phase relationship whereby to excite said antenna in a selected mode, said helically wound conductors being unequally spaced around the support and the feed voltages being selected whereby the voltages appearing on the conductors at the same transverse plane are given by 18 where n l, 2, ...N N total number of helical conductors M the mode number, an integer, for mode M the phase of the radiated electric field varies with the azimuth angle, d), as M for a constant elevation angle 6, and the magnitude of the electric field is essentially independent of the azimuth angle 4), (15,, the angular placement of said transverse plane and wherein the support circumference Bp M cos 25 0.5 p radius of the support B Z-zr/A where A is the wavelength. 6. An elliptically polarized helical antenna with low axial ratio comprising a support having a conductive outer surface, at least two conductors spaced from said surface and helically wound about said surface in the same direction, said conductors wound with a pitch angle greater than 25, means for supporting the helical conductors spaced from said surface, and means for feeding the adjacent end of each of said two or more conductors with voltages of substantially equal magnitude and having predetermined phase relationship whereby to excite said antenna in a selected mode, said helically wound conductors being equally spaced around the support and the exciting voltages being selected whereby the voltages appearing at the same transverse plane are given by where n l, 2, ...N M the mode number, an integer, for mode M the phase of the radiated electric field varies with the azimuth angle, (1:, as Md) for a constant elevation angle 0, and the magnitude of the electric field is essentially independent of the azimuth angle 4). N total number of helical conductors and wherein the support circumference B M cos 25 0.5 p radius of the support B Z'rr/A where A is the wavelength. 7. A helical antenna as in claim 5 wherein the pitch angle and the turn length of the helical conductors are uniform. 8. A helical antenna as in claim 6 wherein the pitch angle and the turn length of the helical conductors are uniform. 9. A helical antenna as in claim 5 wherein the helical conductors are uniformly spaced from the support. 10. A helical antenna as in claim 6 wherein the helical conductors are uniformly spaced from the support. 11. A helical antenna as in claim 5 wherein the helices are uniformly spaced around the support and the turn length is given by where M mode number, an integer p radius of the helix turn ll: pitch angle of helix elevation angle of beam (0 is broadside) B Zrr/A )t wavelength. 12. A helical antenna as in claim 6 wherein the turn length is given by where M mode number. an integer p radius of the helix turn 1!: pitch angle of helix 6 elevation angle of beam 90 is broadside) whereby to radiate a predetermined pattern. Patent Citations
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